Upper Estimate of the Interval of Existence of Solutions of a Nonlinear Timoshenko Equation

1997 ◽  
Vol 4 (3) ◽  
pp. 219-222
Author(s):  
Drumi Bainov ◽  
Emil Minchev
Keyword(s):  
Growth Rate ◽  
Initial Data ◽  
Boundary Value Problem ◽  
Nonlinear Term ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Boundary Value ◽  
Upper Estimate

Abstract Solutions to the initial-boundary value problem for a nonlinear Timoshenko equation are considered. Conditions on the initial data and nonlinear term are given so that solutions to the problem under consideration do not exist for all t > 0. An upper estimate of the t-interval of the existence of solutions is obtained. An estimate of the growth rate of the solutions is given.

scholarly journals The initial boundary value problem of a mixed-typed hemivariational inequality

2001 ◽  
Vol 25 (1) ◽  
pp. 43-52 ◽  
Author(s):  
Guo Xingming
Keyword(s):  
Boundary Value Problem ◽  
Differential Inclusion ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Hemivariational Inequality ◽  
Weakly Continuous ◽  
Decay Of Solutions ◽  
Initial Boundary Value

A mixed-typed differential inclusion with a weakly continuous nonlinear term and a nonmonotone discontinuous nonlinear multi-valued term is studied, and the existence and decay of solutions are established.

FRACTIONAL LANDAU–GINZBURG EQUATIONS ON A SEGMENT

2008 ◽  
Vol 10 (06) ◽  
pp. 1151-1181
Author(s):  
ELENA I. KAIKINA
Keyword(s):  
Global Existence ◽  
Boundary Value Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Global Existence Of Solutions ◽  
Asymptotic Representation Of Solutions ◽  
Representation Of Solutions ◽  
Initial Boundary Value

We study the initial-boundary value problem for the fractional Landau–Ginzburg equations on a segment. The aim of this paper is to prove the global existence of solutions to the inital-boundary value problem and to find the main term of the asymptotic representation of solutions.

The initial–boundary-value problem for real viscous heat-conducting flow with shear viscosity

2003 ◽  
Vol 133 (4) ◽  
pp. 969-986 ◽  
Author(s):  
Dehua Wang
Keyword(s):  
Initial Data ◽  
Boundary Value Problem ◽  
Shear Viscosity ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Heat Conducting ◽  
Large Initial Data ◽  
Viscous Heat ◽  
Initial Boundary Value

An initial–boundary-value problem for the nonlinear equations of real compressible viscous heat-conducting flow with general large initial data is investigated. The main point is to study the real flow for which the pressure and internal energy have nonlinear dependence on temperature, unlike the linear dependence for ideal flow, and the viscosity coefficients and heat conductivity are also functions of density and/or temperature. The shear viscosity is also presented. The existence, uniqueness and regularity of global solutions are established with large initial data in H1. It is shown that there is no shock wave, vacuum, mass concentration, or heat concentration (hot spots) developed in a finite time, although the solutions have large oscillations.

scholarly journals Decay of Small Solutions for the Zakharov-Kuznetsov Equation posed on a half-strip

2011 ◽  
Vol 31 (1) ◽  
pp. 57
Author(s):  
Nikolai Larkin ◽  
Eduardo Tronco
Keyword(s):  
Initial Data ◽  
Boundary Value Problem ◽  
Global Solution ◽  
Exponential Decay ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Small Initial Data ◽  
Half Strip ◽  
Initial Boundary Value

We formulate in a half-strip an initial boundary value problem for the Zakharov-Kuznetsov equation. Assuming the existence of a regular global solution, we prove an exponential decay for small initial data.

Existence of a global smooth solution to the initial boundary-value problem for the p-system with nonlinear damping

2013 ◽  
Vol 143 (6) ◽  
pp. 1243-1253
Author(s):  
Mina Jiang ◽  
Dong Li ◽  
Lizhi Ruan
Keyword(s):  
Initial Data ◽  
Boundary Value Problem ◽  
Smooth Solution ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Damping ◽  
P System ◽  
Global Smooth Solution ◽  
Initial Boundary Value

This paper is concerned with the initial boundary-value problem for the p-system with nonlinear damping. We prove the existence of a global smooth solution under the assumption that only the C0-norm of the derivative of the initial data is sufficiently small, while the C0-norm of the initial data is not necessarily small. The proof is based on several key a priori estimates, the maximum principle and the characteristic method.

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